The banner featured Nottingham Forest owner Evangelos Marinakis holding a gun to the head of midfielder Morgan Gibbs-White, with a speech bubble next to Gibbs-White saying that Marinakis is not involved in any wrongdoing.
The incident occurred during a Premier League match at Selhurst Park on August 24, which ended in a 1-1 draw.
The rivalry between the two clubs has been building since Nottingham Forest was involved in Crystal Palace's demotion to the Europa Conference League earlier in the season.
Nottingham Forest took Crystal Palace's place in the Europa League and will debut in the league phase in late September.
Nottingham Forest has expressed concerns about the banner, and the FA has decided to investigate the matter.